1. Field of the Invention
The present invention relates to a semiconductor light emitting diode (LED), an opto-electronic integrated circuit (OEIC), and a method of fabricating the OEIC; and, more particularly, to an integrated semiconductor, which is in a mixed arrangement with a semiconductor integrated circuit performing an electric signal processing and which integrates a high-brightness LED, a phototransistor capable of controlling optical output power/wavelength with a gate voltage, a silicon laser element, a light receiving element, and a waveguide, and methods of fabricating them.
2. Description of the Related Arts
Optical communications are used in broadband networks supporting the Internet industry. Optical transmission and receiving in the optical communications are made possible by employing Group III-V or Group II-VI compound semiconductor lasers.
Although diverse structures have been suggested for compound semiconductor lasers, a double hetero structure is mostly used. In the double hetero structure, two different kinds of compound semiconductors are joined together by fitting a compound semiconductor with a small band gap into a compound semiconductor with a large band gap. In order to form the double hetero structure, a conductive n-type compound semiconductor, a non-doped i-type compound semiconductor, and a p-type compound semiconductor are sequentially epitaxially grown and laminated in a vertical direction on a substrate. It is then necessary to notice a band structure of the non-doped i-type compound semiconductor sandwiched in between the other two compound semiconductors as it is important that the i-type compound semiconductor has a smaller band gap than the n-type and p-type compound semiconductors, a lower conduction band level than the n-type, and a higher valence band level than the p-type. That is, electrons and holes are confined together in the i-type region. Because electrons and holes are likely to be in the same region, it is highly possible that electrons and holes collide with each other and cause pair annihilation, thereby increasing luminescence efficiency. Moreover, because refractive index tends to increase as the band gap gets smaller, light can also be confined within the i-type compound semiconductor by selecting a material having a refractive index of the i-type compound semiconductor lower than a refractive index of the n-type or p-type compound semiconductor. This confined light efficiently induces or promotes recombination of electrons and holes causing a population inversion, which in turn leads to laser oscillation.
With enhancements in optical communications using an efficient light-emitting compound semiconductor, long distance instantaneous information communications are realized in large quantities. Namely, information processing or saving is carried out on an LSI having a silicon backbone, and information transmission is carried out by a laser having a compound semiconductor used as the backbone.
If silicon can be illuminated at high efficiency, then it is very industrially worthwhile because an electronic device and an LED can be integrated together on a silicon chip. To keep abreast with it, researches on the illumination of silicon have expanded and are in progress.
However, it is difficult to illuminate silicon at high efficiency because silicon has an indirect transition type band structure. In the indirect transition type band structure, either a value of momentum at the lowest conduction band energy or a value of momentum at the lowest valence band energy is not zero. In case of silicon, the lowest energy point of the valence band is a point G where a value of momentum is 0, while the lowest energy point of the conduction band is not the point G but exists between the points G and X. To be more specific, suppose k0=0.85*p/a, where ‘a’ is a lattice constant. Then, it degenerates to 6 points of (0,0,±k0), (0,±k0,0), (±k0,0,0), as shown in FIG. 1A.
Meanwhile, most of compound semiconductors are called direct transition type semiconductors because the conduction band and the valence band respectively have the lowest energy at the point G.
Next, the following will explain why luminescence efficiency is bad in an indirect transition type semiconductor and why luminescence efficiency is good in a direct transition type semiconductor.
As described earlier, in order to illuminate a semiconductor element, electrons and holes collide with each other and are annihilated, and an energy difference of both has to be emitted as a photon or light. At this time, both the energy conservation law and the momentum conservation law must be satisfied. An electron has energy levels within the conduction band, while a hole has energy levels for electronless regions within the valence band. A difference between them becomes light energy. As the wavelengths of light vary depending on energy, an energy difference between the conduction band and the valence band, i.e., the band gap size, determines the wavelength of light, i.e., color. Viewed in this light, there is not much difficulty in the law of energy conservation being satisfied.
Meanwhile, since a collision between electrons and holes is involved in light emission, it is also crucial that momentum is conserved. According to the quantum mechanics that rules the microscopic world, electrons, holes, and photons are not only wavelengths but also elastically scattering particles, so the law of momentum conversation is satisfied. Momentum is a physical quantity which measures how much force is input to make particles fly away from the site of collision. From the perspective of the dispersion relation of light (ω=ck, where ω is an angular frequency, c is a high velocity, and k is momentum of a photon) or the light energy, one can guess that the momentum of a photon during crystallization is almost zero. This means that light collisions may cause a substance to fly away, their impact on the scattering of the substance is very little, which perfectly coincides with our instincts.
On the other hand, a hole has nearly no momentum because its lowest energy point is also at the point G. However, in case of silicon which is an indirect transition type semiconductor, electrons hardly exist at the point G but at the lowest energy point around X. Thus, silicon has a momentum as large as k0=0.85*p/a.
To be short, as far as silicon is concerned, it is impossible to satisfy the momentum conservation law as well as the energy conservation law simply during the electron-hole collisions. Therefore, a phonon which is an oscillating quantum of a photon in crystals was absorbed or emitted to convert only electron-hole pairs into light, trying to satisfy both the momentum and energy conservation laws by any means. Although we are not to imply this mechanism or process does not exist physically, its probability of occurrence is still slim because electrons, holes, photons, and phonons in silicon exhibit a high-dimensional scattering where they collide with each other at the same time. This is primarily why silicon, the indirect transition type semiconductor, is reported to show very poor luminescence efficiency.
On the contrary, a lowest energy point of the conduction band and a lowest energy point of the valence band for most direct transition type compound semiconductors are found at the point G, so the law of momentum conservation and the law of energy conservation are satisfied at the same time. Therefore, luminescence efficiency in compound semiconductors is high indeed.
There has been reported about a transistor laser diode which drives laser in use of a compound semiconductor with a high luminescence efficiency by a bipolar transistor made out of a compound semiconductor (see R. Chan, M. Feng, N. Holonyak, Jr., A. James, and G. Walter, “Applied Physics Letters”, vol. 88, pp. 143508-1-143508-3, 2006).
As mentioned before, even though silicon in the bulk state shows very poor luminescence efficiency, it is also known that the luminescence efficiency increases if silicon is made to a porous state or to nano-sized particles. For example, there is a report that when silicon having been anodized in a hydrofluoric acid solution becomes porous, it emits light at room temperature and in the visible wavelength band (see L. T. Canham, “Applied Physics Letters”, vol. 57, pp. 1046-1048, 1990). The mechanism involved here is not perfectly explained, but many acknowledge the possible importance of the quantum size effect to allow porous silicon to be trapped in a narrow region. Generally, inside a small size silicon, electrons are confined in their regions and do not have a definite amount of momentum, according to the uncertainty principle in quantum mechanics. It is considered that this causes electrons and holes to recombine very easily.
As another way of using silicon, light emitting diode acting as a luminescent element can be fabricated by implanting Er ions during pn junction formed on a Si substrate (see, for example, S. Coffa, G. Franzo, and Priolo, “Applied Physics Letters”, vol. 69, pp. 2077-2079, 1996). When Er ions are implanted into the Si substrate, it creates an impurity orbit which is a spatially localized state. Therefore, if electrons within the conduction band of Si are captured into the impurity orbit, it is possible that their momentums practically become zero and recombine with holes within the valence band to emit light. Since the light emission in result of Er-ion implantation is of a 1.54 μm wavelength, light is likely to propagate without being adsorbed by surrounding silicon. Moreover, this also is a wavelength featuring a low energy loss when a prior art optical fiber is utilized. Therefore, even when technical advances in future may bring a new age of Si-based LEDs using Er ions, many suspect that investment in large-scale facilities will not be necessary because any existing optical network can be employed as it is.
Still another way of using silicon is combining the quantum size effect and the idea of Er-ion for implantation of Er ions into silicon nano-particles, so as to be able to increase luminescence efficiency (see, for example, F.Iacona, G. Franzo, E. C., Moreira, and F. Priolo, “Journal of Applied Physics”, vol. 89, pp. 8354-8356, 2001, or S. Coffa, “IEEE Spectrum”, pp. 44-49, October 2005).
It was a customarily accepted belief about a prior art technique for illuminating silicon that silicon should be put in the porous state or made in nano-size particles according to the quantum size effect, in order to change the structure of a silicon conduction band to the bulk band structure and to lower the momentum from the point k0 according to the uncertainty principle. However, there is a problem that the surface of a nano-sized silicon particle for example is much more likely to be oxidized and silicon dioxide is produced on the surface. As silicon oxide is an insulator with a very large band gap, the silicon dioxide film formed on the surface consequently makes it difficult to efficiently implant electrons or holes. Therefore, although the prior art silicon light emitting diode may be very high in photoluminescence intensity, it certainly is very low in electroluminescence efficiency. In addition, crystallinity of material used for an emissive layer becomes important for light emission, but unlike single crystalline silicon, silicon nano particles obtained by chemical vapor deposition (CVD) or porous silicon having plural irregular pores formed on the surface due to anode oxidation might suffer deterioration in crystallinity. In effect, poor crystallinity may cause light emission through a defect level. However, the light emission using a defect shows poor efficiency, consequently making it unable to fabricate any device that can put itself to a practical use like information communications.
As mentioned before, a variety of approaches have been made to illuminate silicon by porous silicon or nano-size silicon particles or Er doping, but luminescence efficiency has not yet reached a level for practical applications.
In the meantime, as inventors we came to discover that a light emitting diode featuring high luminescence efficiency can easily be formed, through a prior art silicon process, over a Si substrate, the light emitting diode comprising a first electrode for electrons, a second electrode for holes, and a light emitting section electrically connected to the first and the second electrode, wherein the light emitting section is made out of single crystalline silicon and has a first surface (upper surface) and a second surface (lower surface) facing the first surface, and wherein with respect to (100) plane of the first and second surfaces, the light emitting section crossing at right angles to the first and second surfaces is made thinner. First of all, illumination principles and verification results thereof are provided, followed by objects of the present invention for practical applications.
A principle for efficiently illuminating a Group IV semiconductor such as silicon or germanium equivalent thereto will be explained with reference to accompanying drawings.
Wave function ψ(r) indicating electronic states in crystals of silicon and the like can be expressed in the following equation 1 as a best approximation.ψ(r)=φk0(r)ξ(r)  Equation 1
Here, k0 is a momentum that gives a band valley in a conduction band, r=(x,y,z) indicates a position in space, Φk0(r) gives Bloch's relation in a band valley of the conduction band, and ξ(r) is an envelope function. Further, Φk0(r) can be expressed in Equation 2 in terms of a periodic function uk0(r+a)=uk0(r) reflecting periodicity against a unit lattice vector (a) in crystals.φk0(r)=uk0(r)eik0·r  Equation 2
As is evident, it is an atom-scale distance function, highly oscillating. Meanwhile, the envelope function ξ(r) describes slowly-varying components in atom scale, and indicates a response to the physical configuration of a semiconductor or externally applied electric fields. Assuming, including the case of ψ(r) as a wave function in semiconductor structures not necessarily having bulk crystals but finite sizes, a satisfactory formulation of ξ(r) can be induced as follows Equation 3.[ε(k0−i∇)+V(r)]ξ(r)=Eξ(r)  Equation 3
Here, ε=ε(k) indicates a band structure in a bulk of conduction band electrons having the momentum k, in which a sum of a differential operator −i∇ and a momentum k0 are substituted for the momentum k, i.e., ε(k0−i∇). In addition, V=V(r) indicates a potential an electron feels. For instance, if an insulator or a different kind of semiconductor comes in contact with the boundary of a given semiconductor, a potential barrier is made and an electric field is applied by external electric field effects to control a value of V=V(r). For simplicity of description, only changes in z-direction of V are discussed.
For a better understanding, suppose that there is a silicon film formed on a designated plane 100 for a semiconductor. As described before, in a bulk it has a band structure similar to one shown in FIG. 1A, so the valley in a conduction band existing in kz direction (0,0,±k0) is approximate to Equation 4.
                              ɛ          ⁡                      (            k            )                          =                                                                              ℏ                  2                                                  2                  ⁢                                      m                    t                    *                                                              ⁢                              (                                                      k                    x                    2                                    +                                      k                    y                    2                                                  )                                      +                                                            ℏ                  2                                                  2                  ⁢                                      m                    l                    *                                                              ⁢                                                (                                                            k                      z                                        ∓                                          k                      0                                                        )                                2                                              ❘                                    Equation        ⁢                                  ⁢        4            
Here, m*t and m*1 are effective masses in silicon crystals obtained respectively from a curvature in a direction of the long axis and the short axis for a conduction band valley having a rotary ellipse shape.
Also, Equation 3 may be substituted into Equation 4 to get Equation 5.
                                          [                                                            -                                                            ℏ                      2                                                              2                      ⁢                                              m                        t                        *                                                                                            ⁢                                  (                                                            ∂                      x                      2                                        ⁢                                          +                                              ∂                        y                        2                                                                              )                                            -                                                                    ℏ                    2                                                        2                    ⁢                                          m                      l                      *                                                                      ⁢                                                      ∂                    z                    2                                    ⁢                                      +                                          V                      ⁡                                              (                        r                        )                                                                                                                  ]                    ⁢                      ξ            ⁡                          (              r              )                                      =                              E            ⁢                                                  ⁢                          ξ              ⁡                              (                r                )                                              ❘                                    Equation        ⁢                                  ⁢        5            
By applying the envelope function to Equation 6, Equation 5 can be written in the form Equation 7, provided that (x,y) denotes a direction parallel to the (100) plane, W is a width, and L is a length.
                              ξ          ⁡                      (            r            )                          =                                                            ⅇ                ⅈ                            ⁡                              (                                                                            k                      x                                        ⁢                    x                                    +                                                            k                      x                                        ⁢                    y                                                  )                                                    LW                                ⁢                      χ            ⁡                          (              z              )                                                          Equation        ⁢                                  ⁢        6                                                      [                                          -                                                      ℏ                    2                                                        2                    ⁢                                          m                      l                      *                                                                                  ⁢                                                ∂                  z                  2                                ⁢                                  +                                      V                    ⁡                                          (                      z                      )                                                                                            ]                    ⁢                      χ            ⁡                          (              z              )                                      =                  Δ          ⁢                                          ⁢          E          ⁢                                          ⁢                      χ            ⁡                          (              z              )                                                          Equation        ⁢                                  ⁢        7            
Here, ΔE is energy in the z-direction, and all electron energies measured from the bottom of a conduction band can be expressed in Equation 8.
                    E        =                                                                              ℏ                  2                                ⁢                                  k                  x                  2                                                            2                ⁢                                  m                  t                  *                                                      +                                                            ℏ                  2                                ⁢                                  k                  y                  2                                                            2                ⁢                                  m                  t                  *                                                      +                          Δ              ⁢                                                          ⁢              E                                ❘                                    Equation        ⁢                                  ⁢        8            
First of all, it is confirmed that Equation 7 reproduces bulk electronic states. To this end, an answer in continuous state when V(r)=0 may be obtained. This can be confirmed in that with a thickness t as the z-direction, an envelope wave function is then written as shown in Equation 9, and ΔE is as expressed in Equation 10.
                              χ          ⁡                      (            z            )                          =                              1                          t                                ⁢                      ⅇ                          ⅈ              ⁢                                                          ⁢                              k                z                            ⁢              z                                                          Equation        ⁢                                  ⁢        9                                          Δ          ⁢                                          ⁢          E                =                                                            ℏ                2                            ⁡                              (                                                      k                    z                                    ∓                                      k                    0                                                  )                                      2                                2            ⁢                          m              l              *                                                          Equation        ⁢                                  ⁢        10            
That is, the wave function oscillates severely in a continuously spread state over the entire bulk crystals. At this time, a quantum mechanical expected value of the momentum in the z-direction naturally becomes Equation 11, kz being a momentum operator in the z-direction.
                                                                                          〈                                                            k                      ^                                        z                                    〉                                =                                  ∫                                                                                    ⅆ                        3                                            ⁢                      r                                        ⁢                                                                                  ⁢                                                                  ψ                        *                                            ⁡                                              (                        r                        )                                                              ⁢                                          (                                                                        -                          i                                                ⁢                                                  ∂                          z                                                                    )                                        ⁢                                          ψ                      ⁡                                              (                        r                        )                                                                                                                                                                    =                                                      k                    z                                    ±                                      k                    0                                                                                      ❘                            Equation        ⁢                                  ⁢        11            
As is clear from the equation, in an indirect transition type semiconductor such as silicon, the probability of electrons being far away from the point G in momentum space is overwhelmingly high, which means that electrons move with great momentum.
The present invention is based on facts that if an ultra-thin film having a thickness ‘t’ in the z-direction, the fact that a direct transition type semiconductor in a bulk changes practically into a direct transition type semiconductor by quantum confined effects is used as a basic principle. More details are followed.
For a better understanding, suppose that silicon has a very small thickness ‘t’ in the z-direction and an insulator made out of SiO2 for example with a large band gap is nearby on the top and bottom along the z-direction to be in contact with vacuum of a great energy barrier or the air. The same effects can be expected by trapping electrons in a narrow area under the influence of the electric field effect for example. In these cases, the wave function of electrons in silicon becomes zero on a vertical interface of the z-direction. Although technically there is always a possibility that effusion of the quantum mechanic wave function exists, because a large energy barrier reduces the effusion exponentially with respect to the distance in the z-direction, the assumption that wave function of electrons in silicon becomes zero on the interface is almost correct in the strict sense. Therefore, even if an externally applied potential is V(r)=0, protons in the envelop function are completely different from a case where ‘t’ is large. In effect, an envelope wave function for quantum-confined electrons and holes can be explained in Equation 12 if n indicating an exponent indicating a discrete energy level is an even number (n=0,2,4, . . . ), while expressed in Equation 14 if n is an odd number (n=1,3, 5 . . . ) regardless of whether the value of an energy level is an even number of an add number.
                                          χ            n                    ⁡                      (            z            )                          =                                            2              t                                ⁢                      cos            ⁡                          (                              π                ⁢                                  z                  t                                ⁢                                  (                                      n                    +                    1                                    )                                            )                                                          Equation        ⁢                                  ⁢        12                                                      χ            n                    ⁡                      (            z            )                          =                                            2              t                                ⁢                      sin            ⁡                          (                              π                ⁢                                  z                  t                                ⁢                                  (                                      n                    +                    1                                    )                                            )                                                          Equation        ⁢                                  ⁢        13                                          Δ          ⁢                                          ⁢          E                =                                                            ℏ                2                                            2                ⁢                                  m                  l                  *                                                      ⁢                                          π                2                                            t                2                                      ⁢                                          (                                  n                  +                  1                                )                            2                                ❘                                    Equation        ⁢                                  ⁢        14            
Needless to say, the energy level is the lowest when n=0. To plot an envelope wave function, the origin of the z-axis was set up as a center of thin film silicon and it was assumed that there existed an interface having an energy barrier of z=±t/2. Before getting into further details, the nature of the envelope wave function Xn(z) will be explained first. In case n is zero or an even number, the wave function becomes symmetric with respect to symbol changes in z, i.e., Xn(z)=Xn(−z). In this example, it is said that the parity is even. On the other hand, in case n is an odd number, the wave function behaves as Xn(z)=−Xn(−z). In this example, it is said that the parity is odd.
Because of this symmetric structure, the evaluation of the envelope wave function's contribution to momentum yields Equation 15 below.
                                                                                          〈                                                            χ                      n                                        ⁢                                                                                                                  k                          ^                                                z                                                                                    ⁢                                          χ                      n                                                        〉                                =                                  ∫                                                            ⅆ                                                                        zx                          n                          *                                                ⁡                                                  (                          z                          )                                                                                      ⁢                                          (                                                                        -                          i                                                ⁢                                                  ∂                          z                                                                    )                                        ⁢                                                                  χ                        n                                            ⁡                                              (                        z                        )                                                                                                                                                                    =                0                                                    ❘                            Equation        ⁢                                  ⁢        15            
This shows a well-known nature that if Xn(z) is differentiated with respect to the z-direction, the original parity of Xn(z) is changed, so it becomes zero when integrated with respect to the z-direction. After all, since electrons are strongly trapped along the z-direction, the envelope wave function becomes a standing wave where electrons do not move at all. This is totally contradictory to Equation 9 where the envelope wave function is an exponential function in the silicon bulk state and electrons move the entire bulk crystals with great momentum. One thing to be careful, though, is that all wave functions having taken Bloch functions into consideration are built up by substituting Equation 2, Equation 6 and Equation 13 or Equation 14 into Equation 1, so quantum mechanical expected values of momentum in the z-direction yield Equation 16.
                                                                                          〈                                                            k                      ^                                        z                                    〉                                =                                  ∫                                                                                    ⅆ                        3                                            ⁢                      r                                        ⁢                                                                                  ⁢                                                                  ψ                        *                                            ⁡                                              (                        r                        )                                                              ⁢                                          (                                                                        -                          i                                                ⁢                                                  ∂                          z                                                                    )                                        ⁢                                          ψ                      ⁡                                              (                        r                        )                                                                                                                                                                    =                                  ±                                      k                    0                                                                                      ❘                            Equation        ⁢                                  ⁢        16            
Namely, if an original semiconductor material is in bulk, the valley of a conduction band is not found at the point G but as (0,0,±k0), so the wave function overall reflects this nature. That is, although electrons seem to be able to move with momentum ±k0 even in a thin-film semiconductor material, one should be careful to draw hasty conclusions. For example, in case a material is inversely symmetric in crystals like silicon, the valley (0,0,+k0) and the valley (0,0,−k0) are energically equivalent and degenerated. As in this example, when a quantum mechanical state having a degenerated energy level in general is confined to the spatially same area, hybridization occurs between these states. In other words, if there is an energy bond connecting the valley (0,0,+k0) and the valley (0,0,−k0) even for an instant, two discrete levels form a bound orbit and a non-bound orbit. For example, the Coulomb interaction between electrons (this has not been much included in band calculation) works rather strongly between electrons trapped in a narrow area. The interactions between electrons are called an electron correlation and known to cause serious problems including many transit metal oxides such as a high-temperature superconductor. However, this reflects that, in the bulk silicon, sp orbit of an original silicon atom is big, and this fortunately has not caused any serious problems so far. However, when electrons are trapped in a very narrow area where quantum mechanic effects play a crucial role, the Coulomb interaction becomes so strong that it cannot be ignored. Meanwhile, if elements of a Hamiltonian matrix are to be calculated taking the Coulomb interaction into consideration, hybridization occurs in connection between the valley (0,0,+k0) and the valley (0,0,−k0). And, diagonalization of the Hamiltonian matrix exhibits the formation of split orbits, i.e., a bound orbit and a non-bound orbit. This is similar to a H-atom formation process from two adjacent hydrogen atoms, and evaluation methods on this have been available for about 70 years since the quantum mechanics was established by Heitler-London. In the meantime, we first discovered the formation of a bound state understood by Heitler-London is also important for intervalley bonding especially when Group IV semiconductors such as silicon are confined in a narrow area. Moreover, even though no such energy bond existed at all, it was still possible to produce, through a unitary conversion between two states, a standing wave where electrons do not move in the z-axis direction. The following will provide more details on this.
A Bloch state has a property of U−k0(r)=Uk0(r) due to inversely symmetric crystals, so the Bloch wave function for the valley (0,0,+k0) and the valley (0,0,−k0) can be expressed as Φk0(r)=uk0(r)eik0z and Φ−k0(r)=uk0(r)e−ik0z, respectively. Therefore, the e±ik0z is a part that is going to require attention. For the formation of a new base state using the sum and difference of those wave functions, conversion to Equation 17 preferably takes place based on the unitary conversion U.
                                                                        U                ⁡                                  (                                                                                                              ⅇ                                                      ⅈ                            ⁢                                                                                                                  ⁢                                                          k                              0                                                        ⁢                            z                                                                                                                                                                                        ⅇ                                                                                    -                              ⅈ                                                        ⁢                                                                                                                  ⁢                                                          k                              0                                                        ⁢                            z                                                                                                                                )                                            =                                                1                                      2                                                  ⁢                                  (                                                                                    1                                                                    1                                                                                                                                      -                          i                                                                                            i                                                                              )                                ⁢                                  (                                                                                                              ⅇ                                                      ⅈ                            ⁢                                                                                                                  ⁢                                                          k                              0                                                        ⁢                            z                                                                                                                                                                                        ⅇ                                                                                    -                              ⅈ                                                        ⁢                                                                                                                  ⁢                                                          k                              0                                                        ⁢                            z                                                                                                                                )                                                                                                        =                                                2                                ⁢                                  (                                                                                                              cos                          ⁢                                                                                                          ⁢                                                      (                                                                                          k                                0                                                            ⁢                              z                                                        )                                                                                                                                                                                        sin                          ⁢                                                                                                          ⁢                                                      (                                                                                          k                                0                                                            ⁢                              z                                                        )                                                                                                                                )                                                                                        Equation        ⁢                                  ⁢        17            
Thus, one may learn that a change in the wave function for atomic levels can be expressed in terms of a wave function of two standing waves, i.e., 21/2uk0(r)cos(k0z) and 21/2uk0(r)sin(k0z). And, the entire wave function can be arranged as follows:ψ(r)=√{square root over (2)}uk0(r)cos(k0z)ξ(z)  Equation 18ψ(r)=√{square root over (2)}uk0(r)sin(k0z)ξ(z)|  Equation 19
Reflecting a fact that an expected value of momentum in the z-axis direction is a standing value yields another equation below.
                                                                        〈                                                      k                    ^                                    2                                〉                            =                              ∫                                                      ⅆ                                                                                  ⁢                    z                                    ⁢                                                                          ⁢                                                            ψ                      *                                        ⁡                                          (                      z                      )                                                        ⁢                                      (                                                                  -                        i                                            ⁢                                              ∂                        z                                                              )                                    ⁢                                      ψ                    ⁡                                          (                      r                      )                                                                                                                                              =              0                                                          Equation        ⁢                                  ⁢        20            
Therefore, it is clear that electrons do not move towards the z-axis direction at all. Meanwhile, one should be careful not to misunderstand that an expected value of momentum seems to vary simply by changing the base. In fact, base wave functions like Equation 18 and Equation 19 do not necessarily show intrinsic momentum. That is, matrix elements of a momentum operator may be rearranged as in Equation 21 out of Equation 18 and Equation 19, in which diagonal matrix elements become zero and non-diagonal matrix elements are pure imaginary numbers.
                                          U            ⁡                          (                                                                                          k                      0                                                                            0                                                                                        0                                                                              -                                              k                        0                                                                                                        )                                ⁢                      U                          -              1                                      =                              (                                                            0                                                                      ik                    0                                                                                                                    -                                          ik                      0                                                                                        0                                                      )                    ❘                                    Equation        ⁢                                  ⁢        21            
Whether it is physically appropriate for taking such a base is determined entirely depending on the properties of a target material. Although we assume a very thin single crystalline silicon film which is hardly translation symmetric in the z-axis direction, it is better to take the form of standing waves such as v2uk0(r)cos(k0z) or v2uk0(r)sin(k0z), instead of taking the intrinsic state of momentum such as uk0(r)e±ik0z. When bulk silicon is involved, however, uk0(r)e±ik0z is preferably taken because the bulk silicon is translation symmetric. Moreover, in the bulk state, electrons having momentum ±k0 move very actively inside crystals. At this time, the electrons are strongly scattered by phonons which are oscillating quantum of photons in crystals, and phase of the wave function changes dynamically, so one cannot possibly expect to form the momentum +k0 and the momentum −k0 in a coherent state. On the contrary, a wave function that is sufficiently determined even at room temperature can form a standing wave with fixed phase if a very thin single crystalline silicon film for example where electrons are trapped in an extremely narrow area even thinner than a mean free path 1 controlling a scattering length is employed. In a quantitative sense, it means that a standing wave with a perfect matching or compatible size with the narrow area can be formed while an electron wave moves forwards and backwards at high speed in that narrow area.
As explained so far with reference to simple equations, if electrons are confined in an extremely narrow area as in a very thin single crystalline silicon film, electrons in the bulk state or electrons contained in a material, e.g., silicon, having no electrons of a conduction band at the point G do not move in the vertical direction of the thin film. Again, in the quantitative sense, this means that there is no vertical direction for the thin film, so it is rather natural that the vertical motion of electrons on the thin film is absent. In short, although electrons may have been moving at high speed inside crystals in the bulk state, they come to stop on the thin film because there is eventually going to be no direction for them to move along.
This phenomenon is depicted in a band diagram shown in FIG. 1B. Because no movement can be made towards the z-axis direction, the band structure of bulk shown in FIG. 1A is projected on the plane k2=0, while a band structure shown in FIG. 1B is formed by the application of a thin film or electric field effects. The band structure similar to one shown in FIG. 1B is essential for designing a field effect transistor in use of silicon and a basis of device physics. This two-dimensionally trapped material is called a two-dimensional electric or magnetic field. Further, a one-dimensional electric or magnetic field can also be generated if a cell structure, not the thin film, is employed.
Assuming that the band structure shown in FIG. 1B is used, bulk electrons having been at the valley (0,0,±k0) of FIG. 1A are now found at the point G in FIG. 1B. Therefore, electrons in this state do not move in the z-axis direction.
Returning to the basic of device physics, the inventors reached a concept that electrons existing at the point G in FIG. 1B recombine with holes efficiently and can be used as a light emitting diode. Therefore, since confined electrons are not free to move around, when they collide with small holes with low momentum existing at the point G, light with low momentum are emitted, without violating both the energy conservation law and the momentum conservation law. As mentioned before, momentum is a measure of how much impact is required for scattering a particle upon a particle colliding with another particle. As inventors, we entrapped electrons into a narrow area to immobilize them and observed that the electrons lose momentum in such state. When the momentum of an electron decreases, the momentum conservation law during scattering is satisfied (this was difficult to achieve by prior art techniques), enabling even Group IV such as silicon semiconductors to efficiently emit light.
Based on this concept, a very thin Si film cut into 1 cm×1 cm size was actually formed on a portion of a substrate, and its photoluminescence measurement results are shown in FIGS. 2, 3 and 4B. Particularly, FIG. 2 and FIG. 4B show luminescence intensities as a result of photoluminescence. As is seen from the results, a very strong enhancement in the luminescence intensity is observed in the very thin Si film. This intensity, compared with the luminescence by an indirect transition type bulk silicon semiconductor, is higher by several figures. From this, we came to believe that those trapped electrons in a narrow area make Group IV such as silicon semiconductors change into a direct transition type. FIG. 3 shows a peak wavelength of the spectrum obtained by this experiment. This confirms that a bigger wavelength is obtained as much as an energy level being displayed in form of silicon band gap (Equation 4). This implies that the more energy scatters, the greater the band gap, conforming to the principle of the quantum confined effect explained above. Changes in wavelength excitation in result of increased band gaps are shown in FIG. 4A. As described above, silicon can be illuminated at high efficiency by using the plane 100 as a surface, making the silicon film thinner, and practically setting the point G as a valley of energy.
Next, we performed verification experiments on electroluminescence by fabricating a light emitting diode based on the structure described above.
FIG. 5A-FIG. 5H show cross sectional structures of a light emitting diode in order of fabricating process. In addition, FIG. 6A-FIG. 6H are diagrams showing the fabricating process, seen from the top of an SOI substrate. Here, FIGS. 5A-5H are horizontal cross-sectional views of FIGS. 6A-6H, respectively. For example, FIG. 5H shows a cross-sectional structure of FIG. 6H(a) cut along a plane 13. Moreover, FIG. 7 is a diagram showing a cross-sectional structure of FIG. 6H(a) cut along a plane 14. A complete form of the device is shown in FIGS. 5H, 6H(a) and (b), and 7.
The following sequentially explains a fabricating process.
As shown in FIG. 5A, an SOI (Silicon On Insulator) substrate used as a support base plate is first prepared by sequentially laminating a silicon substrate 1, a buried oxide (hereinafter referred to as BOX) 2, and an SOI layer 3 from the bottom to up. When seen from the top of the substrate, only the SOI layer 3 is seen as shown in FIG. 6A. In fact, if the SOI substrate is substantially thin, one may be able to see through to the bottom substrate during the test. A substrate having a plane orientation 100 is used as the SOI layer 3 made out of single crystalline silicon. An initial film thickness of the tested SOI layer 3 prior to the process was 55 nm. In addition, BOX 2 had a film thickness of about 150 nm.
Next, a resist is coated and exposed by a mask through photolithography, leaving out only a desired region of the resist. An anisotropic dry etching is performed to obtain the mesa-shaped SOI layer 3 as shown in FIG. 5B and FIG. 6B. For simplicity of description, only one element is shown in the drawings, but it would be needless to say that a large number of elements are actually formed over a substrate, and many elements can be integrated at high productivity through the silicon process.
Although not shown in the drawings, the anisotropic dry etching is carried out further to make corners of the mesa-shaped SOI layer 3 round. By rounding the corners, a subsequent oxidation process can be performed entirely including the etched portion where a tensile stress is easily gathered, interfering with the oxidation. If the corners are not removed or rounded, more current flows into this SOI layer 3 because of its relatively greater thickness than other parts and as a result, luminescence efficiency is deteriorated.
In order to protect the surface, the surface of the SOI layer 3 is then oxidized by about 15 nm to form a silicon dioxide film 4 as shown in FIG. 5C and FIG. 6C. The silicon dioxide film 4 not only reduces damages on the substrate caused by ion implantation in the following process, but also controls impurities escaping into the air as a result of activation annealing.
Thereafter, resist patterning is carried out by using photolithography to leave the resist only in a desired region, and BF2 ions are implanted with energy 15 keV and a dose of 1×1015/cm2 to form a P-type impurity implantation region 5 in the SOI layer 3.
After the resist is removed, resist patterning is carried out again by using photolithography to leave the resist only in a desired region, and P ions are implanted with energy 10 keV and a dose of 1×1015/cm2 to form an N-type impurity implantation region 6 in the SOI layer 3. This state is shown in FIG. 5D. The top view of FIG. 5D is provided in FIG. 6D(a). Meanwhile, the ion implanted state is found in FIG. 6D(b) showing the bottom of the silicon dioxide film 4. In effect, when examined through an optical microscope during the fabrication, the silicon dioxide film 4 made out of glass looks clear, while an impurity implanted region as shown in FIG. 6D(b) looks in a slightly different color.
In the ion plantation process, an ion implanted portion on the SOI layer 3 becomes amorphous and is poorly crystallized. Therefore, although not shown in the drawings, it is important to make only the surface of the SOI layer 3 be amorphized and let crystalline silicon remain in an interfacial area between the SOI layer 3 and the BOX 2. Meanwhile, if acceleration voltage for the ion implantation is set too high, all the ion implanted region on the SOI layer 3 is amorphized, so that the single crystallinity may not be restored even under a subsequent annealing process and the SOI layer 3 is polycrystallized. Therefore, after the ion implantation, crystallinity should be restored by activation annealing and the like. As discussed before, having good single crystallinity is a crucial factor for improving luminescence efficiency.
FIGS. 5D and 6D(b) show that the N-type impurity implantation region 6 is formed next to the P-type impurity implantation region 5, but it is not mandatory to put them close by. When the photolithography using a mask is included in the fabricating process, the two regions may be dislocated. In such case, the P-type impurity implantation region 5 and the N-type impurity implantation region 6 are either separated or overlapped with each other. In this example, a mask pattern is carefully selected to purposely leave a non-ion implanted SOI layer 3 between the P-type impurity implantation region 5 and the N-type impurity implantation region 6 at the same time. A diode having such a non-ion implanted region (i-region) is known as a pin diode. A pn diode and a pin diode, each comprising an ultra-thin silicon layer, are fabricated at the same time for an experiment.
Thereafter, the activation annealing is customarily carried out to active impurities and at the same time, the single crystallinity of the damaged region of the SOI layer 3 due to the ion implantation process may be restored. To reduce the number of processes, however, the activation annealing is not included for the fabricating process in this example, so the impurities are activated at the same time with an oxidation treatment. The reduced number of processes also opens up possibilities for reducing the fabricating cost. Here, the activation and annealing for restoring the single crystallinity may be included as well.
Next, a silicon nitride film 7 is deposited on the front face to a thickness of 100 nm, leading to a state shown in FIGS. 5E and 6E.
Then, resist patterning is carried out by using photolithography to leave the resist only in a desired region. The silicon nitride film 7 is then processed by anisotropic dry etching, leading to a state shown in FIGS. 5F and 6F.
A cleansing process is carried out, followed by an oxidation treatment to make a desired region of the SOI layer 3 as thin as possible. Here, conditions for oxidation are very important. As inventors, we learned that under a prior art oxidation treatment at a temperature of 1000° C. or below, which is often used as the silicon process, the thickness of a silicon dioxide film formed on the P-type impurity implantation region 5 differs by up to twice the thickness of a silicon dioxide film formed on the N-type impurity implantation region 6. As explained above, the SOI layer 3 needs to be even thinner than the mean free path 1 to enhance luminescence efficiency. For example, the mean free path 1 of silicon is about 10 nm at room temperature. Therefore, the film thickness of the SOI layer 3 has to be 10 nm or less, preferably 5 nm or less. In order to produce a thin, evenly spread film, using impurity ions having different oxidation rates by conductive regions are not allowed. With different oxidation rates, if a conductive region on one side is 5 nm thick, a conductive region on the other side may become too thick or all of it may be oxidized and destroyed. In the meantime, we discovered that even when a 100 nm thick oxide needs to be formed under dry oxidation treatment at an oxidation temperature of 1000° C., a difference between the thickness of the silicon dioxide film formed on the P-type impurity implantation and the thickness of the silicon dioxide film formed on the N-type impurity implantation region 6 may be reduced as small as 1 nm or so.
In this example, an approximately 90 nm-thick silicon dioxide film 8 was formed by the dry oxidation treatment at 1100° C. Consequently, it was possible to reduce the film thickness of an ultra-thin silicon layer to about 5 nm. Moreover, the difference between the film thickness of the N-type doped region and the film thickness of the P-type doped region could be suppressed to 1 nm or less. During the oxidation treatment, one has to watch the film thickness of an ultra-thin silicon layer through a spectrum ellipsometry with an ultra-precision of 1 nm or less, while carefully checking the film thickness of the other silicon layer. For mass production, it is preferred that an oxidation device has a built-in ellipsometry. Moreover, a wafer to be fabricated may preferably have a pre-set pattern for use in film thickness testing. As the luminous region of FIGS. 2 and 3 shows, a pattern for about 1 cm2-size testing is provided within a wafer, so as to thoroughly check a film thickness distribution in the wafer surface, while carrying out the oxidation treatment at the same time. In addition, since 1100° C. is high enough to activate ions, impurities that are introduced through ion implantation by this oxidation treatment are readily activated to form a P-type SOI region 9, an N-type SOI region 10, a P-type ultra-thin silicon region 11, and an N-type ultra-thin silicon region 12. This state is shown in FIGS. 5G and 6G, respectively.
Thereafter, the silicon nitride layer 7 is removed by a cleaning process and by wet etching with hot phosphoric acid. Then, the hydrogen annealing treatment is carried out at a temperature of 400° C., and any bonds produced during the process are H-terminated. FIG. 5H depicts a full cross-sectional view of a finished light emitting diode product. FIG. 6H(1) is a top view of FIG. 5H, and FIG. 6H(b) is a bottom view of the silicon dioxide layer 8 to show an implantation pattern. FIG. 7 is a diagram showing the light emitting diode cut along the plane 14. In detail, FIG. 7 illustrates the formation of the silicon dioxide layer 8 as a result of oxidation of side walls adjacent to the N-type ultra-thin silicon region 12.
Finally, a desired wiring is carried out to complete the formation of a high-efficiency silicon light emitting diode on the silicon substrate 1.
FIG. 8 diagrammatically shows how to measure LED properties having the structure described above. A probe 15 is connected to the P-type SOI region 9, while a probe 16 is connected to the N-type SOI region 10. Diode properties can be obtained by flowing current between the probe 15 and the probe 16. A threshold value of the current-voltage characteristics reflects an increment of the band gap shown in FIG. 4A. A proportional dependence of band gap shown in FIG. 4A on the film thickness was observed even in film thicknesses of the P-type and N-type ultra-thin silicon regions 11 and 12 which are differently designed as 13.6 nm, 6.3 nm, 4.0 nm, and 1.3 nm. FIG. 4B shows a spectrum by photoluminescence. As is evident from the drawing, as the SOI film thickness in the ultra-thin silicon region decreases, the luminescence intensity sharply increases. And, luminescence 17 occurs, as shown in FIG. 8, in the P-type ultra-thin silicon region 11, the N-type ultra-thin silicon region 12, and an interface therebetween. For a better understanding, the luminescence 17 overlapped with an upper portion of the P-type ultra-thin silicon region 11 and an upper portion of the N-type ultra-thin silicon region 12 is not shown, but it is needless to say that luminescence 17 takes place on the upper portions as well. The luminescence 17 also proceeds in a direction parallel to the substrate, as illustrated in FIG. 8.
Next, FIGS. 9A-9F respectively shows a contrast luminescent image superimposed with an optical image of a device element being photographed at the same time, under forward bias conditions applying bias voltages of 0, 1, 2, 3, 4, and 5V to the PN junction, where the image is. Here, the element has a width W of 100 μm and an ultra-thin silicon film has a length L (sum of lengths of the P-type ultra-thin silicon region 11 and the N-type ultra-thin silicon region 12) of 10 μm. A grayish band portion in the vertical direction between the probe 1 and the probe 2 in FIG. 9A is an area where the P-type ultra-thin silicon region 11 and the n-type ultra-thin silicon region 12 are formed. Even though luminescence intensities are observed in many areas, the luminescence intensity from an area with the P-type ultra-thin silicon region 11 and the N-type ultra-thin silicon region 12 is definitely stronger, while the luminescence intensity from the relatively thin P-type or N-type SOI region 9 or 10 on the SOI layer is almost zero. These results coincide with the principle discussed earlier that bulk silicon has very week luminescence intensity and the luminescence intensity increases if an ultra-thin silicon layer is employed. In effect, when the number of CCD-observed photons excited from light emission was counted, the luminescence intensity from an ultra-thin silicon layer was definitely larger by several figures than that of a thick silicon layer. Moreover, when luminescence was spectroscopically analyzed by using an insert-filter, it turned out the luminescence intensity was highest around the 1000 nm wavelength and lowest around the 500 nm wavelength. This indicates that light emission in this case is the result of recombination due to the band gap in an ultra-thin silicon layer, not by radiation from a photoelectron and the like having a large kinetic energy, and verifies the principle discussed before is indeed correct.
Next, FIGS. 10A-10F respectively show an image photographed by a low magnification lens under forward bias conditions applying 0, 5, 10, 20, 30, and 40V. Again, it turned out that luminescence intensity was strong from the P-type ultra-thin silicon region 11 and the N-type ultra-thin silicon region 12, being spread onto a concentric circle.
By using this structure, it becomes possible to obtain a device demonstrating high luminescence efficiency and good productivity and having a Group IV semiconductor as a basic component formed over a silicon substrate for example.